In our first experiment, we tackle the problem of alignment of unstructured random graphs across different graph sizes. We compare the alignment quality, as well as the execution time of different algorithms and filters. In particular, for each predefined graph size between 10 and 100, we perform 50 repetitions of aligning two random Erdos-Renyi graphs using the following algorithms: Gromov-Wasserstein (GW) [1]}, with graphs compared based on their shortest path matrices, as proposed in [2]}; three algorithms solving for the original GOT cost: the original stochastic GOT algorithm, as proposed in [3]}, and our fGOT and stochastic fGOT algorithms, using the corresponding low pass filter \(g(L) = \sqrt{L^{\dagger }}\) ; and two algorithms solving for a high-pass filter cost: fGOT and stochastic fGOT with \(g(L) = L^2\) .
